Nuclear medicine is a unique medical specialty wherein radiation is used to acquire images which show the function and anatomy of organs, bones or tissues of the body. Radiopharmaceuticals are introduced into the body, either by injection or ingestion, and are attracted to specific organs, bones or tissues of interest. Such radiopharmaceuticals produce gamma photon emissions which emanate from the body and are captured by a scintillation crystal, with which the photons interact to produce flashes of light or “events.” Events are detected by an array of photodetectors, such as photomultiplier tubes, and their spatial locations or positions are calculated and stored. In this way, an image of the organ or tissue under study is created from detection of the distribution of the radioisotopes in the body.
One particular nuclear medicine imaging technique is known as Positron Emission Tomography, or PET. PET is used to produce images for diagnosing the biochemistry or physiology of a specific organ, tumor or other metabolically active site. Measurement of the tissue concentration of a positron emitting radionuclide is based on coincidence detection of the two gamma photons arising from positron annihilation. When a positron is annihilated by an electron, two 511 keV gamma photons are simultaneously produced and travel in approximately opposite directions. Gamma photons produced by an annihilation event can be detected by a pair of oppositely disposed radiation detectors capable of producing a signal in response to the interaction of the gamma photons with a scintillation crystal. Annihilation events are typically identified by a time coincidence between the detection of the two 511 keV gamma photons in the two oppositely disposed detectors, i.e., the gamma photon emissions are detected virtually simultaneously by each detector. When two oppositely disposed gamma photons each strike an oppositely disposed detector to produce a time coincidence event, they also identify a line of response, or LOR, along which the annihilation event has occurred. An example of a PET method and apparatus is described in U.S. Pat. No. 6,858,847, which patent is incorporated herein by reference in its entirety.
After being sorted into parallel projections, the LORs defined by the coincidence events are used to reconstruct a three-dimensional distribution of the positron-emitting radionuclide within the patient. In two-dimensional PET, each 2D transverse section or “slice” of the radionuclide distribution is reconstructed independently of adjacent sections. In fully three-dimensional PET, the data are sorted into sets of LORs, where each set is parallel to a particular detector angle, and therefore represents a two dimensional parallel projection p(s, φ) of the three dimensional radionuclide distribution within the patient, where s corresponds to the distance along the imaging plane perpendicular to the scanner axis and φ corresponds to the angle of the detector plane with respect to the x axis in (x, y) coordinate space (in other words, (φ corresponds to a particular LOR direction). Coincidence events are integrated or collected for each LOR and stored as a sinogram. In this format, a single fixed point in f(x,y) traces a sinusoid in the sinogram. In each sinogram, there is one row containing the LORs for a particular azimuthal angle φ; each such row corresponds to a one-dimensional parallel projection of the tracer distribution at a different coordinate along the scanner axis. This is shown conceptually in FIG. 1.
An event is registered if both crystals detect an annihilation photon within a coincidence time window τ (e.g., on the order of 4-5 ns), depending on the timing properties of the scintillator and the field of view. A pair of detectors is sensitive only to coincidence events occurring in the volume between the two detectors, thereby eliminating the need for physical collimation, and thus significantly increasing sensitivity. Accurate corrections can be made for the self-absorption of photons within the patient (i.e., attenuation correction) so that accurate measurements of tracer concentration can be made.
The number of time coincidences detected per second within a field of view (FOV) of a detector is the count rate of the detector. The count rate at each of two oppositely disposed detectors, A and B, can be referred to as singles counts, or singles, SA and SB. The time required for a gamma photon to travel from its point of origin to a point of detection is referred to as the time of flight, or TOF, of the gamma photon. TOF is dependent upon the speed of light c and the distance traveled. A time coincidence, or coincidence event, is identified if the time difference between the arrival of signals in a pair of oppositely disposed detectors is less than a coincidence time window τ.
As illustrated in FIG. 2, if an annihilation event occurs at the midpoint of a LOR, the TOF of the gamma photon detected in detector A (TA) is equal to the TOF of the gamma photon detected in detector B (TB). If an annihilation event occurs at a distance Δx from the midpoint of the LOR, the difference between TA and TB is Δt=2Δx/c, where c is the speed of light. If d is the distance between the detectors, the TOF difference Δt could take any value from −d/c to +d/c, depending on the location of the annihilation event.
Time-of-flight (TOF) positron emission tomography (PET) (“TOF-PET”) is based on the measurement of the difference Δt between the detection times of the two gamma photons arising from the positron annihilation event. This measurement allows the annihilation event to be localized along the LOR with a resolution of about 75-120 mm FWHM, assuming a time resolution of 500-800 ps (picoseconds). Though less accurate than the spatial resolution of the scanner, this approximate localization is effective in reducing the random coincidence rate and in improving both the stability of the reconstruction and the signal-to-noise ratio (SNR), especially when imaging large objects.
TOF scanners developed in the early 1980s were used for research and clinical applications, but the SNR gain provided by the TOF measurements of about 500 ps resolution was offset by the low stopping power of the BaF2 and CsF scintillation crystals used in such scanners. Image reconstruction for complete 2D TOF-PET data has been disclosed in the prior art. Early TOF scanners used a back project-then-filter (BPF) algorithm. The maximum-likelihood estimation algorithm (MLEM) also was adapted for list-mode TOF data, and shown to provide improved image quality compared to BPF. The increased computation required to process the TOF data also led to the proposal of a faster iterative algorithm that was directly applied to the back-projected TOF data.
In contrast with 2D TOF reconstruction, few studies have been devoted to the 3D case, probably because the rise of 3D PET in the late 1980s overshadowed the interest for TOF. The Colsher filter and the 3D re-projection algorithm for axially truncated data generalized the 3D back projection filtered methods to TOF data.
However, the spatial resolution and sensitivity offered by those TOF systems could not compete with the values achieved with BGO scanners. As a result, TOF-PET almost completely disappeared from the scene in the 1990s. Today, faster electronics and crystals such as LSO and LaBr3 reopen the prospect of exploiting the TOF information without compromising other parameters such as the count rate, the sensitivity, and the energy and spatial resolutions. This prospect motivates the present invention of fast reconstruction strategies for 3D TOF-PET.
However, while extending MLEM or MAP (Maximum A posteriori Probability) algorithms to 3D TOF-PET is conceptually straightforward, the computational load is an issue, because the number of data bins is now equal to the number of LORs (which exceeds 108 in 3D PET even after axial undersampling using the ‘span’ concept) multiplied by the number of sampled TOF bins. What is needed is a feasible approach for reconstruction of 3D TOF-PET data.